α-Reflexive Rings with Involution

• Muna E. Abdulhafed

  Department of Mathematics, Faculty of Science, Azzaytuna University, Tarhunah, Libya

  Author

• Aafaf E. Abduelhafid

  Department of Mathematics - Faculty of Education, Azzaytuna University, Tarhunah, Libya

  Author

This paper studies the concept of the -quasi-*-IFP (resp.,  -*-reflexive) *-rings, as a generalization of the quasi-*-IFP (resp., *-reflexive) *-rings and every quasi-*-IFP (resp., *-reflexive) *-ring is  -quasi-*-IFP (resp., -*-reflexive). This paper also discusses the sufficient condition for the quasi-*-IFP (resp., *-reflexive) *-ring in order to be -quasi-*-IFP (resp., -*- reflexive). Finally, this study investigates the -quasi-*-IFP (resp., -*-reflexivity) by using some types of the polynomial rings.

Abdulhafed, M. E. (2019). A Study of Reflexive and Reversible Rings with Involution (Unpublished Doctoral disserta-tion). Faculty of Science -Alexandria University.

Aburawash, U. A. (1997). On Embeding of Involution Rings.pdf. Mathematica Pannonica, 8(2), 245–250.

Aburawash, U. A., & Abdulhafed, M. E. (2018a). On reflexive rings with involution. International Journal of Algebra, 12(3), 115–132.

Aburawash, U. A., & Abdulhafed, M. E. (2018b). On reversibility of rings with involution. East-West J. of Mathematics, 20(1), 19–36.

Aburawash, U. A., & Saad, M. (2014). On Biregular, IFP and Quasi-Baer ∗ -Rings. East-West J. of Mathematics Mathematics, 16(2), 182–192.

Aburawash, U. A., & Saad, M. (2016). *-Baer property for rings with involution. Studia Scientiarum Mathematicarum Hungarica, 53(2), 243–255.

Aburawash, U. A., & Saad, M. (2019). Reversible and reflexive properties for rings with involution. Miskolc Mathematical Notes, 20(2), 635–650.

Başer, M., Harmanci, A., & Kwak, T. K. (2008). Generalized semicommutative rings and their extensions. Bulletin of the Korean Mathematical Society, 45(2), 285–297.

Başer, M., Hong, C. Y., & Kwak, T. K. (2009). On extended reversible rings. Algebra Colloquium, 16(1), 37–48.

Başer, M., & Kwak, T. K. (2010). Extended semicommutative rings. Algebra Colloquium, 17(2), 257–264.

Hong, C. Y., Kwak, T. K., & Rizvi, S. T. (2006). Extensions of generalized armendariz rings. Algebra Colloquium, 13(2), 253–266.

Kim, N. K., & Lee, Y. (2003). Extensions of reversible rings. Journal of Pure and Applied Algebra, 185(1–3), 207–223.

Martindale, W. S., & 3rd. (1969). Rings with involution and polynomial identities. Journal, of Algebra, 11, 186–194.

Zhao, L., & Zhu, X. (2012). Extensions of α-reflexive rings. Asian-European Journal of Mathematics, 5(1), 1–10.

• PDF

Copyright (c) 2021 Muna E. Abdulhafed, Aafaf E. Abduelhafid

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright of the articles Published by Almukhtar Journal of Science (MJSc) is retained by the author(s), who grant MJSc a license to publish the article. Authors also grant any third party the right to use the article freely as long as its integrity is maintained and its original authors and cite MJSc as the original publisher. Also, they accept the article remains published by the MJSc website (except in the occasion of a retraction of the article).